No it doesn't. What would the benefit be of allowing this type of restriction?
Private and protected inheritance is good for encapsulation (information hiding). Protected* inheritance is supported in C++, although it isn’t in Java. Here’s an example from my project where it would be useful.
There is a base class in as 3rd party framework**. It has dozens of settings plus properties and methods for manipulating them. The base class doesn’t make a lot of checking when individual settings are assigned, but it will generate an exception later if it encounters an unacceptable combination.
I’m making a child class with methods for assigning these settings (e.g. example, assigning carefully crafted settings from a file). It would be nice to deny the rest of the code (outside my child class) the ability to manipulate individual settings and mess them up.
That said, I think in C++ (which, again, supports private and protected inheritance) it's possible to cast the child class up to parent and get access to parent's public members. (See also Chris Karcher's comment in this thread.) Still, protected inheritance improves information hiding. If members of a class B1 need to be truly hidden within other classes C1 and C2, it can be arranged by making a protected variable of a class B1 within C1 and C2. Protected instance of B1 will be available to children of C1 and C2. Of course, this approach by itself doesn't provide polymorphism between C1 and C2. But polymorphism can be added (if desired) by inheriting C1 and C2 from a common interface I1.
* For brevity will use "protected" instead of "private and protected".
** National Instruments Measurement Studio in my case.